Riemannian Geometry
Manfredo P. do Carmo
Riemannian Geometry - A book resource
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More resources on Riemannian Metrics
nLab: Riemannian Geometry
Comprehensive wiki entry with references.
John M. Lee Book Companion
Free sample chapters and errata for Riemannian Manifolds.
Differential Geometry
Explore Riemannian metrics & differential geometry with MIT's George Lusztig. Learn key concepts in this comprehensive course.
Lectures on Riemannian Geometry
Explore Riemannian metrics with Frederic Schuller's "Lectures on Riemannian Geometry." Learn the foundations in this comprehensive course!
mathworld.wolfram.com
MathWorld is an extensive online encyclopedia of mathematics from Wolfram that provides detailed, readable articles on mathematical concepts, definitions, and theorems. It covers topics from algebra and geometry to differential geometry (including Riemannian metrics), offering formulas, examples, and references.
ocw.mit.edu
MIT OpenCourseWare provides free, openly licensed MIT course materials across disciplines. It includes lecture notes, assignments, exams, and video lectures from math and differential geometry courses that cover topics such as Riemannian metrics.